9.16 In regard to inconsistencies presented by the azimuthal angle \( \phi \), as discussed in Problem 9.15 , it has been pointed out by \( W \). Louisell \( { }^{8} \) that more consistent angle variables are \( \sin \phi \) and \( \cos \phi \).
(a) Show that
\[
\begin{array}{l}
{\left[\sin \phi, \hat{L}_{z}\right]=i \hbar \cos \phi} \\
{\left[\cos \phi, \hat{L}_{z}\right]=-i \hbar \sin \phi}
\end{array}
\]
